Kit Library / Science / એકમો અને માપન
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. The bites below come from this kit — swipe through them in the app.
No unit? Your answer means nothing.
A physical quantity is fully expressed only when a numerical value is paired with a unit. The same number means different things with different units.
↳ Magnitude and unit are inseparable — always write both.
Seven base units build everything else.
↳ Memorise the 7 base units — every derived unit traces back to them.
One mnemonic, all seven units.
Use "My Kind Teacher Always Keeps Me Calm" for the 7 SI base units in order:
↳ M-K-T-A-K-M-C locks in all seven base units.
Dimensions reveal a quantity's true nature.
The dimensional formula expresses a quantity in terms of the base dimensions M (mass), L (length), T (time) and others.
↳ Write dimensions as powers of M, L, T — this unlocks all of dimensional analysis.
One technique, three exam-winning powers.
Dimensional analysis is a shortcut tool with three major applications:
↳ Check, convert, derive — dimensional analysis does all three.
Angle has no dimension — but it has a unit.
↳ Dimensionless and unitless are not the same thing.
These have no M, L, or T at all.
↳ Any ratio of like quantities is dimensionless — a frequent SSC CGL question.
Know exactly what the exam tests.
↳ Dimensional formulas + SI units = guaranteed marks in SSC CGL.
Independent vs built-from-others.
↳ 7 fundamentals generate every derived quantity in physics.
A missing unit crashed a Mars orbiter.
↳ Unit errors cause real disasters — always double-check units.
Derive any formula in seconds.
↳ Define → substitute → simplify — dimensions in 3 steps.
It can't do everything — know the limits.
↳ Dimensional analysis checks and derives — but doesn't replace full physics.
The last physical artefact retired.
Until 2019, the kilogram was defined by a platinum-iridium cylinder kept in France. Since 20 May 2019, it is defined by the Planck constant — making all SI base units based on fundamental constants.
↳ Modern SI units rest on constants of nature, not physical objects.
Convert any unit with one formula.
↳ n₁u₁ = n₂u₂ is the master conversion equation.
Three basics unlock this topic.
↳ Algebra + SI prefixes + basic quantities = ready for dimensions.
Units and dimensions form the foundation of all physical measurement. This topic covers the SI system, fundamental and derived units, dimensional formulas, and the powerful technique of dimensional analysis used to check…
Full explanation, worked examples & memory tricks in the app
All 17 questions, laddered from warm-up to topper-level, each with its answer and the reasoning behind it.
Q1. Which of the following is a physical quantity?
BeginnerD · 9.8 m/s²
A physical quantity has both a numerical value and a unit. 9.8 m/s² has both; the others are pure numbers.
Q2. How many base units are there in the SI system?
BeginnerA · Seven
The SI system has exactly seven base units: metre, kilogram, second, ampere, kelvin, mole, and candela.
Q3. The dimensional formula of force is:
BeginnerA · [M L T⁻²]
Force = mass × acceleration, so [M] × [L T⁻²] = [M L T⁻²].
Q4. Which of these is a derived unit?
BeginnerB · newton
Newton is formed from base units: kg·m/s². The others are base units.
Q5. A student writes the speed of a car as 60. What is missing?
BeginnerD · A unit
A physical quantity needs a unit. '60' alone does not specify km/h, m/s, or mph.
Q6. The SI system has exactly seven base units, and all other units are derived from them.
BeginnerA · True
The SI system has exactly seven base units, and all other units are derived from them.
Q7. Which pair of quantities has the same dimensions?
IntermediateD · Work and torque
Work and torque both have dimensions [M L² T⁻²], though they are different physical quantities.
Q8. The principle of homogeneity states that in a correct equation:
IntermediateB · The dimensions of all terms on both sides must be equal.
Homogeneity means dimensional consistency: every term in a valid physical equation must have the same dimensions.
Q9. Which of the following CANNOT be determined by dimensional analysis?
IntermediateD · The value of a dimensionless constant like ½
Dimensional analysis cannot find dimensionless numerical constants; it only checks dimensions.
Q10. 1 newton is equal to how many dynes?
IntermediateD · 10⁵ dyne
1 N = 1 kg·m/s² = 1000 g × 100 cm/s² = 10⁵ g·cm/s² = 10⁵ dyne.
Q11. The dimensional formula of pressure is:
IntermediateA · [M L⁻¹ T⁻²]
Pressure = force/area = [M L T⁻²] / [L²] = [M L⁻¹ T⁻²].
Q12. Which of the following is dimensionless?
IntermediateB · Strain
Strain is a ratio of lengths, so it has no dimensions. Angle, refractive index, and relative density are also dimensionless.
Q13. In the equation $s = ut + \frac{1}{2}at^2$, which term has dimensions [L]?
IntermediateA · All three terms
By homogeneity, each term must have dimension [L]: $s$ is length, $ut$ is velocity×time, and $at^2$ is acceleration×time².
Q14. A quantity has dimensions [M L² T⁻³]. Which physical quantity is it?
AdvancedC · Power
Power = work/time = [M L² T⁻²] / [T] = [M L² T⁻³].
Q15. Which of the following statements about units and dimensions is correct?
AdvancedA · The dimension of force is the same in SI and CGS.
Dimensions are independent of the unit system. Force has dimension [M L T⁻²] in both SI and CGS, though units differ (newton vs dyne).
Q16. A student claims that because work and torque have the same dimensions, they are the same physical quantity. What is the best response?
AdvancedB · The student is wrong; same dimensions do not imply same physical quantity.
Dimensional analysis cannot distinguish between quantities with the same dimensions. Work and torque are different concepts despite sharing [M L² T⁻²].
Q17. A student is tasked with determining the dimensions of a physical quantity defined as the rate of change of momentum with respect to time, expressed as \( F = rac{dp}{dt} \). Given that momentum \( p \) has dimensions \( [M L T^{-1}] \), what are the dimensions of this physical quantity?
AdvancedC · [M L^2 T^{-2}]
The dimensions of the rate of change of momentum with respect to time can be found by dividing the dimensions of momentum \( [M L T^{-1}] \) by the dimensions of time \( [T] \). Thus, \( [F] = [M L T^{-1}] / [T] = [M L T^{-2}] \), which corresponds to the dimensions of force.
31 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Word Match
Built from this kit's own content
True False
Built from this kit's own content
Memory Match
Built from this kit's own content
Flashcard Battle
Built from this kit's own content
Speed Quiz
Built from this kit's own content
Guess Term
Built from this kit's own content
Sequence Builder
Built from this kit's own content
Categorization
Built from this kit's own content
Revision Battle
Built from this kit's own content
Playable in the app
The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.